Electronic musical scale generator employing a single master oscillator

ABSTRACT

For use in electronic organs and the like, an electronic circuit for generating 12 signals, the frequencies of which correspond to the notes of the musical scale, comprises a single, variable frequency oscillator which produces pulses at a high repetition rate. A counting network, driven by the oscillator pulses, produces 12 pulse trains, the frequencies of which are related to each other by 12 2. The 12 pulse trains are filtered directly to produce musical notes, and are further reduced in frequency, and then filtered to produce lower octaves.

I United States Patent [72] lnventor Robert R. Reyers 709 Magnalia Ave.,Absecon, NJ. 08201 [21] Appl. No. 798,347

[22] Filed Feb. 11, 1969 [45] Patented .lune29, 1971 [54] ELECTRONICMUSICAL SCALE GENERATOR EMPLOYING A SINGLE MASTER OSCILLATOR PrimaryExaminer D. Duggan Assistant Examiner-Stanley J. Witkowski Attorney.lohnF. A. Earley ABSTRACT: For use in electronic organs and the like, anelectronic circuit for generating 12 signals, the frequencies of whichcorrespond to the notes of the musical scale, comprises a single,variable frequency oscillator which produces pulses at a high repetitionrate. A counting network, driven by the oscillator pulses, produces 12pulse trains, the frequencies of 1'. which are related to each other byV2. The 12 pulse trains are filtered directly to produce musical notes,and are further reduced in frequency, and then filtered to produce loweroctaves.

{20 OS I LATOR u an COUNTER COUNTS TO I085 21 B 42 u BIT COUNTER COUNTST0 n49 m A 10 an COUNTER coum's TO 609 2 F A 4% i 10 an COUNTER COUNTSTO 645 94 P c 44 u an coumsn couurs TO 1367 gm 6 w i a an COUNTER coum'sTO 181 19g F i 10 BIT couurea coums TO 767 L1 F i 10 an COUNTER couu'rsT0 813 E E #9 10 an couuren coum's TO as: liqj 0 i 6 BIT COUNTER couu'rsTO 57 L 1 0 k -l u an COUNTER coum's TO 1933 H C PATENTEDJUN29|971 sum 2BF 2 m9 N9 d R mt ow; N. p R? mm; R W J -J m 3.. mm: .w R f 3 31 n T 1 nN: m H m: B $1 T 0 Y r R B -2 ow: mn 3; mm: 02. mm; mm: $5 m1 .1 h: E II I .t w v NNK mow oh 3753 55:8 .5 0. 8 -w w k mm H W n N UK N 5552: 1 wr 8 n H H O O O 0 O O 0 Nm :1. 4| 1 IM-( F. w k Nwwmrk ow E. 8 N on mm 1mm 891 ATTORNEY BACKGROUND OF THE INVENTION This invention relates toimprovements in electronic scale generation for musical instruments, andmore particularly to an apparatus for generating a complete scale ofmusical notes in which the absolute pitch of the notes can be variable,but in which the frequency ratios between the various notes in the scalecannot change.

The tempered musical scale consists of 12 fundamental notes (indecreasing frequency from C through C sharp) which do not have a simplearithmetic relationship. Notes in octaves above and below a selectedscale, however, are harmonic multiples or submultiples of thecorresponding notes in the selected scale. Thus, once the basic scale 12notes is generated, octaves of this scale can be obtained by frequencydivision or multiplication.

Previous methods of generating the notes of the scale have involved theuse of elaborate electromechanical rotating assemblies, or have involvedthe use of 12 or more individually tuned oscillator circuits. A majordisadvantage of the rotating assembly method is the complexity and bulkof the various multispeed gears, rotating members and pickup coils, andin addition, the difficulty of raising or lowering the absolute pitch ofthe scale. In the case of individually tuned oscillator circuits, agingtemperature changes and other factors cause a gradual change in theindividual oscillator frequencies so that they no longer have the properrelationship to each other. This necessitates frequent retuning of theoscillator circuits.

Furthermore, if it is desired to raise or lower the absolute pitch ofthe scale in order to accompany other musical instruments, it isnecessary to retune each of the oscillator circuits individually.

In the prior art, while frequency dividers have been used to producelower octaves, all of the notes in a single octave have never beenproduced by frequency division of the signal produced by a singleoscillator.

SUMMARY OF THE INVENTION In accordance with this invention all of thenotes in a particular octave, preferably the fourth or fifth octaveabove middle C, are produced by a counter network, which receives as itsinput the pulses produced by a single high frequency oscillator. Acounter comprising a chain of flip-flops is provided for each note inthe octave, and each of the counters is preset to provide one voutputpulse for a particular number of input pulses produced by theoscillator. The counter network is preferably designed so that certainof the chains of flip-flops receive their inputs from flip-flops inother chains. In this way, redundant flip-flops are eliminated.

Each of the signals produced by the counter network corresponds to anote in the highest octave, Corresponding notes in the lower octaves areproduced by delivering each of the signals to an additional flip-flopchain. The pulse outputs of the flip-flops chains in the counter networkand the pulse outputs of the flip-flops in the additional flip-flopchains are shaped and filtered to produce signals which can then beamplified to produce a musical tone. Alternatively, the output of aflip-flop chain in the counter network and the outputs of the flip-flopsin the additional flip-flop chain can be combined by addition to producea staircase waveform which is then filtered and amplified to produce amusical note.

. The principal object of the invention is to provide a musical scalegenerator which will produce a scale of electronically generated noteswhich are locked together in frequency and which cannot get out of tunewith each other. An additional object is to provide a musical scalegenerator which will permit raising or lowering of the absoluteoperation of a single control.

pitch of the scale by the I BRIEF DESCRIPTION OF THE DRAWINGSDESCRIPTION OF THE PREFERRED EMBODIMENT Before describing in detail thespecific embodiment of the invention, some theoretical requirements ofmusical scale generation should be considered.

The tempered musical scale consists of the notes C sharp, D, D sharp, E,F, F sharp, G, G sharp, A, A sharp, B and C. From these notes, lower orhigher octaves can be derived by frequency division or multiplication,or additional scale generators can be used. The frequencies of any twoadjacent [2 notes are related by a constant multiplier which is the \/iNumerically, this is an irrational number having value of apl2proximately 1.05946309. The \/2 will be referred to hereafter as 1:.Thus, the frequency ofD is k times the frequency of C sharp, etc. It istherefore the ratios of frequencies that establish the condition ofnotes being in tune with each other, and not their absolute frequencies.As mentioned above, one of the purposes of this invention is to keep theratios of the notes or tones of the scale constant and locked together.Since the ratio of adjacent note frequencies in a scale is an irrationalnumber, the tolerance or accuracy required in the generated tones mustbe established. It has been shown that the average person can detecttone differences (errors) of about 0.69 percent, while the bestperformance in a group of excellent musicians was 0.023 percent. (C. E.Seashore, Psychology of Music, McGraw-Hill, 1938.) The degree ofaccuracy provided by this invention is proportional to the number ofstages in the counters in the counter network. Thus, the accuracyrequired can be readily met.

Referring to FIG. 1, oscillator 20 is a fixed or variable frequencyoscillator of conventional design which produces pulses continuously atits output. For purposes of this description, the frequency of theoutput of oscillator 20 will be assumed tobe 4.286473 mI-Iz. Thefrequency of the output of oscillator 20 will be referred to as f, andit will be understood that f can be varied throughout a wide range, andthat, in alternative embodiments f can be several times 4.286 mHz.

The output pulses of oscillator 20 are delivered through lines 22 and 24to a counter comprising chain of flip-flops generally indicated as 26.Counter 26 comprises 10 flip-flops connected in cascade so that, at theoutput terminal 28 of the highest order flip-flop 30 a pulsetrain isproduced having a frequency of f/2. This frequency corresponds to C, thehighest note on the scale. If the oscillator frequency is 4.286473 mIIz.then C is 4.286473/1024 or 4186.009 Hz.

An ll-bit counter 32 is preset to produce one pulse at its outputterminal 34 for every 1085 oscillator pulses in line 22 to which theinput of counter 32 is connected. Counters 36, 38 and 40 are similar tocounter 32, each comprising a chain of 11 flip-flops connected incascade. Counter 36 produces a pulse at terminal 42 for every 1 149oscillator pulses; counter 38 produces a pulse at terminal 44 for every1367 oscillator pulses; and counter 40 produces a pulse at terminal 46for every 1933 oscillator pulses.

In order to illustrate the manner in which the above-mentioned countersare preset to counts which are not powers of 2, reference is made toFIG. 2, in which the binary flip-flops chain of counter 38 is shown ingreater detail. The input to the first flip-flop in the chain is derivedfrom the oscillator through line 50. The llflip-flops are connected incascade, the 1 output of each of the lower order flip-flops beingconnected to the input of the next higher order flip-flop. Switching ofa flipflop occurs when the preceding flip-flop switches from i to 0. Thel output of each flip-flops 48. 52, 54, 56, 58, 60 and 62 are eachconnected to the cascade of a diode of a group of diodes indicated at 64which act as an AND gate. The outputs of flip-flops 70, 72, 74 and 76are connected to the cathodes of diodes in group 64. The anodes of thediodes are connected in common and through resistor 66 to a positivesupply terminal 68. The common connection of the anodes of the diodes isalso connected through line 78 to the input of an inverter 80. Theoutput of inverter 80 is connected through line 82 to resettingterminals of flip-flops 48,52, 54, 56, 58, 60 and 62. The output toterminal 44 is derived from the l terminals of flip-flops 76 and 62through an OR gate comprising diodes 84 and 86, the cathodes of whichare connected in common to terminal 44 and through a resistor 88 to anegative supply terminal 90. v

t It will be apparent that the circuitry just described establishes acondition such that all of the flip-flops in counter 38 are reset to 0when positive signals appear at the cathodes of all of the diodes ingroup 64. This condition occurs when flip-flops 48, 52, $4, 56, 58, 60and 62 are in the 1 condition and flip-flops 70, 72, 74 and76 are in the0 condition. This corresponds to a count of 1367 oscillator pulses. Whenthis count is reached, all of the flip-flops in the counter are reset tothe 0 condition. The outputs of flip-flops 76 and 62 are con ncctedthrough diodes 84 and 86 to terminal 44. Diodes 84 and 86 along withresistor 88 act as an OR gate so that the voltage at terminal 44 becomesmore positive if either or both of flip-flops 76 and 62 are in the 1condition. Although the output of the last flip-flop 62 has a duty cycleof about 25 percent as a result of the presetting, the output signal atterminal 44 has a duty cycle of about 62 percent. The OR gate insuresthat there is a high amplitude of fundamental frequency content in theoutput at terminal 44.

It will be apparent from the above description how the remainingcounters in the counter network in FIG. I can be preset to any desiredcount. Alternative methods of presetting flip-flops chains to desiredpredetermined counts can be used as well. For example, the ilip=flops inthe chain can be arranged so that some are set to l and others are setto 0 on the occurrence on the change of state of the highest order flipflop. In such an arrangement. the preset count would be the differencebetween the initial count immediately following the change of stated thehighest order flip flop and 2N power where N is the number offlip=ilops. Qther methods of presettlng the binary counter chainsinvolving high order bit translation and selective gating are well knownand can be used as well.

Returning to FIG. 1, l0=bit counters, 9.2, 94. 96, 98 and 100 are presetso that they count to the various counts indicated in the drawing. Theirinputs are derived through. line 102 from the output of the lowest orderflip=ilop in counter 26. An 8-bit counter, which is preset to count to181, is indicated at 106. its input is derived through line 108 fromflip flop ill), which is the third lowest order flip=flcp in counter 26.A 6=bit counter, which is preset to count to 57, derives its inputthrough line 114 from fllp=flop 116., which is the fifth lowestsdstfhtflsshreassess. -..,.o

celcu= Percent True lstsd Bounded Counted frequency frequency countE-Qllill trequensy error etc: N isssocs 1,024 1.02%. sussoos moo a.3,951.00? unease 1,930 assures =o.n1o sin. ,7 1.14s. 01 1,249 arsenal+0.0st f it. {53. a, 9.272 o. ,.s. .1 .srs i. s =oloos rt. ssssstslsisiss i... *2 r 0.011 r rs 1.ass..r 1. can a 70-: inseam 1.6. .os1 sa. e this lsnirzs oiooa In FIG. 1, the notes produced by the variouscounters are indicated at the right of the output terminals.

in order to illustrate the operation of the apparatus shown in FIG. 1,reference is made to the following table, in which the true frequenciesof the notes of the scale (based on a frequency for A of 3520.000 Hz.)are compared with the frequencies at thggggpt tsof the various counters.

It will be noted that the maximum error is well below that which can bedetected by the average person, and is nearly as low as the smallesterror detectable by the best musician in a group of excellent musicians.

As will be apparent from the table, the counters and their preset countswere determined by the first choosing an oscillator frequency which willproduce the true frequency of the note C when divided by 2 or 1024. Thechosen oscillator frequency was 4.286473 mI-Iz. From this chosenoscillator frequency, the divisors necessary to produce the truefrequencies of the other notes were calculated. These divisors are shownin the calculated count column of the table. The divisors were roundedto the integers shown in the rounded count column of the table, and thecounted frequency was calculated.

Certain of the rounded counts are divisible by powers of two. Forexample, the rounded counts for A, G sharp, F, E,

and D sharp are divisible by two. Because of this, in counters 92, 94,96 98 and 100, an lith flip-flop is unnecessary. Flipflop 104 inflip-flop chain 26 takes the place of the unnecessary I 1th flip-flop ineach of these counters.

The preset count of 1448 for the note F sharp is divisible by 2".Accordingly, counter 106 requires only eight flip-flops, the division by2 being accomplished by flip-flops 104, 118 and 110 in flip-flop chain26.

The rounded count for the note D is 1824. This is divisible by 2 andaccordingly counter 112 requires only six flip-flops. A division of 2 isaccomplished by flip-flops 104, 118, 110, and 116 of flip-flop chain 26.

Thus, the arrangement shown in FIG. 1 results in the saving of 13flipflops in the counter network while the maximum frequency error isonly 0.035 percent. If greater errors were tolerated, still moreflip-flops could be eliminated. If closer tolerances were desired, ahigher oscillator frequency could be used which would be divided bycounters having greater numbers of flip-flops.

By reducing the number of flip-flops in a flip-flop chain, the resettingcircuitry is simplified. in fact, the flip-flop chains in the 10, and 86-bit counters can be preset by well-known techniques much simpler thanthat illustrated in FIG. 2 since the input frequencies are lower,permitting slower resetting.

A further reduction of the number of flip-flops in the counter networkcan be obtained by a more extensive use of flip-flops which are commonto several counters. For example, counters 92, 94, 98 and 100 providecounts which are divisible by 3. A common 2-bit counter, preset todivide by 3 could be arranged to receive the output of flip-flop 104,and the number of flip-flops in each of counters 92, 94, 98 and 100could be reduced by two for a net reduction of six flip-flops.

In another technique for reducing the number of flip-flops in thecounter network, a single flip-flop chain could be used to produce twoor more notes by obtaining signals at appropriate counts through the useof conventional decoding networks. For example, an ll-bit counterconnected to receive the output of flip-flop 104 could be preset tocount to 1626. A first decoder could be connected to respond at countsof 813 and 1626 to produce the note E. A second decoder could beconnected to respond at counts of 542, 1084 and 1626 to produce the noteB. The note B would then have a The outputs provided by the counternetwork in FIG. 1 are in the highest octave and are in the form ofrectangular pulses having various duty cycles. When the frequencies aredivided down to produce the lower octave notes, square waves areproduced having no even harmonics. The ideal waveform for electronicmusical note production is the sawtooth. It contains both even and oddharmonics, and the magnitudes of the harmonies are inverselyproportional to the harmonic number. F165. 3 and 4 illustratealternative circuits for producing sawtooth waveforms in the loweroctaves.

Referring particularly to FIG. 3, a circuit is shown for converting theoutput of counter 92 to produce sawtooth waveforms in the highest octaveand in seven lower octaves. Line 122 delivers the output of counter 92to a chain of cascaded flip-flops including flip-flops 124, 126, 128,130, 132, 134 and 136. The rectangular waveform produced by counter 92is delivered through line 122 also to the input of a shaping circuitindicated generally at 138. A capacitor 140 is connected between line122 and the base of a transistor 142. A resistor 144 is connectedbetween the base of the transistor and ground. The emitter is connectedto ground, and the collector is connected throughresistor 146 to apositive supply. A capacitor 148 shunts the collector and emitter, andan output is delivered from the junction between the collector andcapacitor 148 through line 150 to output terminal 152. Similar shapingcircuits 154, 156, 158, 160, 162, 164 and 166 receive the outputs of therespective flipflops 124 through 136 and deliver their outputs toterminals 168 through 180 respectively.

Capacitor 140 differentiates the rectangular waveform in line 122.Capacitor 148 charges through resistor 146. When the differentiatedsignal at the base of transitor 142 is positive, capacitor 148 isdischarged through the transistor. As a result, a sawtooth waveform isproduced at terminal 152. Sawtooth waveforms are also produced atterminals 168 through 180, the waveforms corresponding to the note A insuccessively lower octaves.

Circuits similar to that shown in FIG. 3 may be provided for each of thecounters shown in FIG. 1.

Referring to FIG. 4, an alternative method of producing a sawtoothwaveform is illustrated. The output of counter 92 is delivered throughline 182 to a chain of flip-flops comprising flip-flops 184 through 196.The signal in line 182 is delivered through a resistor 198 to a line200. The output of flip-flop 184 is delivered through a second resistor204 to line 200, and the outputs of the remaining flip-flops aredelivered respectively through other resistors to line 200. Line 200 isconnected to an output terminal 214 and through resistor 212 to ground.

Resistor 198 has approximately twice the resistance of resistor 204, andresistor 204 has approximately twice the resistance of the nextresistor, and so on.

In its essence, the circuit is an adder which combines the added signalsin inverse proportion to their frequencies. A repeating staircasewaveform is produced at terminal 214, and it resembles a sawtooth in itsharmonic content.

The fundamental frequency of the note A at terminal 214 is the seventhsubharmonic of the frequency at the output of counter 92. The higheroctave notes of A are, ofcourse, produced by additional adding networkshaving their resistors connected to the outputs of appropriateflip-flops of the group 184-196. For example, the fourth subharmonicwould be produced by a circuit having resistors combining the outputs offlip-flops 184, 186, 188 and 190 and the output of counter 92.

In summary, the invention produces signals corresponding to notes in ascale, which are locked together so that they cannot get out of tunewith each other. Additional octaves of the 'basic scale can be obtainedby frequency division or by oscillator, and, even though this adjustmentis made, the various notes in the scale will remain in the properrelationship to each other. Accordingly, tuning of the individual notesof an instrument having a scale generator in accordance with theinvention is unnecessary. Although numerous flip-flops are used in thebasic scale generator, a significant number of flip-flops are eliminatedby deriving the inputs to individual counters from higher orderflip-flops of another counter.

I claim:

1. Apparatus for generating alternating audiofrequency electricalsignals corresponding to the notes of a musical scale comprising amaster oscillator for producing a master alternating electrical signalat a frequency above the audio range,

a network comprising at least 12 counters, each comprising a pluralityof cascaded stages of frequency-dividing means,

each of said counters having an output line connected to the output ofits last stage, and an input line connected to the input of its firststage,

said network including means connected to receive the master alternatingelectrical signal and delivering to each said input line'an alternatingelectrical signal to which the frequency of said master signal has anintegral multiple relationship,

at least all but one of said counters having means for sensing a firstpredetermined condition of their stages and resetting said stages to asecond predetermined condition when said first predetermined conditionis reached to establish a scale of each counter such that the signalsonthe output lines are related to each other by integral powers oftheU2.

2. Apparatus according to claim 1 in which said master oscillatorincludes means for varying the frequency of said master alternatingelectrical signal.

3. Apparatus according to claim 1 in which each of said counterscomprises a plurality of flip-flops connected in cascade for successivedivisions by two of the frequency at the input to each flip-flop.

4. Apparatus according to claim 1 including a plurality of frequencydividing means each having an input terminal connected to receive thealternating output signal at one of the output lines in said network,each said frequency dividing means having at least one output terminaland providing an output signal at its output terminal having a frequencywhich is a subharmonic of the frequency of the signal at the inputterminal of said dividing means related to the frequency of said signalat the input terminal by an integral power of two.

5. Apparatus according to claim 1 in which the input line of at leastone of said counters is connected to the output of a stage of anothercounter in said network.

6. Apparatus for generating alternating audiofrequency electricalsignals corresponding to the notes of a musical scale comprising amaster oscillator for producing a master alternating electrical signalat a frequency above the audio range,

a network comprising at least 12 counters, each comprising a pluralityof cascaded stages of frequency-dividing means,

each of said counters having an output line connected to the output ofits last stage, and an input line connected to the input of its firststage,

said network including means connected to receive the master alternatingelectrical signal and delivering to each said input line an alternatingelectrical signal to which the frequency of said master signal has anintegral multiple relationship, and I i,

said network also including means for establishing a scale of eachcounter such that the signals on the output lines are related to eachother by integral powers of Q2.

7. Apparatus according to claim 6 in which said master oscillatorincludes means for varying the frequency of said master alternatingelectrical signal. V. n 8; Apparatus according to claim 6 in which eachof said counters comprises a plurality of-flip-flops connected incascade for successive divisions by two of the frequency at the input toeach flip-flop.

9. Apparatus according to claim 6 including a plurality of frequencydividing means each having an input terminal connected to receive thealternating output signal at one of the output lines in said network,each said frequency dividing means having at least one output terminaland providing an output signal at its output terminal having a frequencywhich is a subharmonic of the frequency of the signal at the inputterminal of said dividing means related to the frequency of said

1. Apparatus for generating alternating audiofrequency electricalsignals corresponding to the notes of a musical scale comprising amaster oscillator for producing a master alternating electrical signalat a frequency above the audio range, a network comprising at least 12counters, each comprising a plurality of cascaded stages offrequency-dividing means, each of said counters having an output lineconnected to the output of its last stage, and an input line connectedto the input of its first stage, said network including means connectedto receive the master alternating electrical signal and delivering toeach said input line an alternating electrical signal to which thefrequency of said master signal has an integral multiple relationship,at least all but one of said counters having means for sensing a firstpredetermined condition of their stages and resetting said stages to asecond predetermined condition when said first predetermined conditionis reached to establish a scale of each counter such that the signals onthe output lines are related to each other by integral powers of the
 122. 2. Apparatus according to claim 1 in which said master oscillatorincludes means for varying the frequency of said master alternatingelectrical signal.
 3. Apparatus according to claim 1 in which each ofsaid counters comprises a plurality of flip-flops connected in cascadefor successive divisions by two of the frequency at the input to eachflip-flop.
 4. Apparatus according to claim 1 including a plurality offrequency dividing means each having an input terminal connected toreceive the alternating output signal at one of the output lines in saidnetwork, each said frequency dividing means having at least one outputterminal and providing an output signal at its output terminal having afrequency which is a subharmonic of the frequency of the signal at theinput terminal of said dividing means related to the frequency of saidsignal at the input terminal by an integral power of two.
 5. Apparatusaccording to claim 1 in which the input line of at least one of saidcounters is connected to the output of a stage of another counter insaid network.
 6. Apparatus for generating alternating audiofrequencyelectrical signals corresponding to the notes of a musical scalecomprising a master oscillator for producing a master alternatingelectrical signal at a frequency above the audio range, a networkcomprising at least 12 counters, each comprising a plurality of cascadedstages of frequency-dividing means, each of said counters having anoutput line connected to the output of its last stage, and an input lineconnected to the input of its first stage, said network including meansconnected to receive the master alternating electrical signal anddelivering to each said input line an alternating electrical signal towhich the frequency of said master signal has an integral multiplerelationship, and said network also including means for establishing ascale of each counter such that the signals on the output lines arerelated to each other by integral powers of 12
 2. 7. Apparatus accordingto claim 6 in which said master oscillator includes means for varyingthe frequency of said master alternating electrical signal.
 8. Apparatusaccording to claim 6 in which each of said counters comprises aplurality of flip-flops connected in cascade for successive divisions bytwo of the frequency at the input to each flip-flop.
 9. Apparatusaccording to claim 6 including a plurality of frequency dividing meanseach having an input terminal connected to receive the alternatingoutput signal at one of the output lines in said network, each saidfrequency dividing means having at least one output terminal andproviding an output signal at its output terminal having a frequencywhich is a subharmonic of the frequency of the signal at the inputterminal of said dividing means related to the frequency of said signalat the input terminal by an integral power of two.
 10. Apparatusaccording to claim 6 in which the input line of at least one of saidcounters is connected to the output of a stage of another counter insaid network.
 11. Apparatus according to claim 6 in which said meansestablishing a scale of each counter effects production of a musicaloctave in 12 of said output lines.